How can I mirror an object once in positive and negative X/Y axis?
The simplest way is to use a mirror modifier. With your object selected, in the Properties panel, click the Modifiers button. It only appears when an object is selected, and looks like this:



In that menu, click the dropdown that says 'Add Modifier' and select 'Mirror'.

There are several options here. You can check X and Y, and depending on how your objects are supposed to look, you might want to enable some of the other options. You'll want to experiment a little to find the settings you want.

You can also use the eyedropper on the bottom right of the modifier box to select an object to use as the center for the operator. Here, I have selected a small sphere I placed at the center, and used it to mirror a Suzanne head on the x and y axes:

Modifier panel:



Result: